Why doesn't an if constexpr make this core constant expression error disappear?

The standard doesn't say much about the discarded statement of an if constexpr. There are essentially two statements in [stmt.if] about these:

1. In an enclosing template discarded statements are not instantiated.
2. Names referenced from a discarded statement are not required ODR to be defined.

Neither of these applies to your use: the compilers are correct to complain about the constexpr if initialisation. Note that you'll need to make the condition dependent on a template parameter when you want to take advantage of the instantiation to fail: if the value isn't dependent on a template parameter the failure happens when the template is defined. For example, this code still fails:

template <typename T>
void f() {
    constexpr int x = -1;
    if constexpr (x >= 0){
        constexpr int y = 1<<x;
    }
}

However, if you make x dependent on the type T it is OK, even when f is instantiated with int:

template <typename T>
void f() {
    constexpr T x = -1;
    if constexpr (x >= 0){
        constexpr int y = 1<<x;
    }
}
int main() {
    f<int>();
}

Note that for the statement discarded by Constexpr If:

the discarded statement can't be ill-formed for every possible specialization:

To fix the issue you can make the statement depending on the template parameter, e.g.

template<typename T, int X> struct dependent_value { constexpr static int V = X; };

template <typename T>
void foo() {
    constexpr int x = -1;
    if constexpr (x >= 0){
        constexpr int y = 1 << dependent_value<T, x>::V;
    }
}

LIVE

I'm not sure why you expect the branch to not be checked. The only time an if branch is "not checked" is when it is part of a template and not instantiated, as per [stmt.if]p2:

During the instantiation of an enclosing templated entity (Clause 17), if the condition is not value-dependent after its instantiation, the discarded substatement (if any) is not instantiated.

Your code doesn't seem to be in a situation where this applies.